If sin A 12 A in quadrant IV what is tan 2A write your answ

If sin A = -1/2, A in quadrant IV, what is tan 2A? (write your answer as a fraction or whole number with NO SPACES, i.e., -sqrt(2)/2) Rewrite as a function of a single angle. Use * for degrees. sqrt((1+cos 76*)/2)

Solution

tan 2A =  2tanA/ (1tan^2 A)

sinA = -1/2

so A = 360* - 30*

A =330* (* degree)

so tan(A) =tan(330)

= -1/sqrt(3)

tan 2A =  2tanA/ (1tan^2 A)

tan2A = 2. -1/sqrt(3) / (1 - (1/sqrt(3)^2 )

= -2/sqrt(3) / (1-1/3)

= -2/sqrt(3)/2/3

= -3/sqrt(3)

= -sqrt(3)

2).

sqrt[ (1+cos76*)/2) = sqrt[ (1 +cos(90 - 14) )/2 ]

but cos(90-x) =sinx

so sqrt[ (1+cos76*)/2) = sqrt( (1+sin14*)/2 )